Sunday, 31 January 2016

Small-town Hockey Phenomenons

There is a book on my shelf, Passionate Minds, full of interviews of top scientists in their fields. Chapter 5 contains an extended passage from biotechnologist Leroy Hood that caught me.

...important were the opportunities that I had in the form of three outstanding High School teachers in a very small town in northern Montana...what was unusual about these teachers is they all cared about students as individuals...Maybe this is a consequence of just small towns, but if you're good in a small town, everybody knows it and you have enormous self-confidence about, gee, this is wonderful, I can really do all these things.

His second observation moves from my later talking points, but it's worth noting nonetheless:

I get [the best students] from small towns...Or I get them from places like New York City where, if they're number one, they know they're the best. I never got anybody that was any good from suburbia...There isn't a push to excel; there isn't the positive reinforcement.

My intrigue lies mainly in that first quote. But ironically enough, scientific talent is rather hard to quantify. I had the idea had to search where all the best scientists come from. But that fell flat, as the concept 'best scientist' is too subjective (and often too historical; Newton, Einstein, etc). Contemporary lists of sorted scientific talent are rare, and I hate using h-indexes (as secretly everyone does).

Sports is another matter. Rankings are all modern, and critics do not shy away from choosing favourites. I live in Canada, and, moreover, hockey is a sport at which Canadians excel. Consider the number of Canadians on the all-time points list (only 3 of the top 20 are from other countries). Roughly half of the league is Canadian; it was notable when at the 2015 season debut, it was revealed slightly less than half of the NHL was Canadian the first time, ever. Hence we dominate both in quality and quantity.

Since I am more familiar with Canadian geography than other places, I chose NHL to use as an example finding out, where exactly does the talent come from.
First consider three of greatest players in history (as measured by career points scored): Wayne Gretzky, Mark Messier, and Gordie Howe. Gretzky grew up in Brantford, ON. Brantford has a modern population of 93,000. Messier grew up in St Albert AB, with a smaller population still of 61,000. Finally Howe, was born in Floral SK (now considered a ghost town; pop. 0?), then grew up in Saskatoon (pop. 206,000, or more relevantly 50,000 in 1930s). For a contemporary example we have Sydney Crosby, who grew up in Cole Harbour, NS, with a population of 25,000.

What interests me here is that:

a) talent, be it intellectual or physical, appears to come disproportionately from smaller towns
b) The NHL appears to be a prime example of this trend
c) The anecdotal observations made here can be quantified.

To establish a baseline, let us imagine that NHL talent is distributed randomly among the Canadian provinces. Provinces are a coarser resolution than cities, but am easy start. I obtained my list of hockey players, and the towns/regions they come from quanthockey.com.

A total of 4673 Canadians have played in the NHL (give or take) since it came into existence almost 100 years ago. If players were homogeneously mixed among our citizens, then we'd expect their prevalence to be in proportion to the provincial population (yay alliteration). For instance, given that Ontario has 13 million residents, or 39% of Canada's population, then we'd expect 4673*0.39 = 1800 NHL players to have been born in Ontario. In fact, there have been 2059 players so far. Ontario is slightly 'enriched' in talent. I haven't corrected for relative population changes over time, however changes are relatively minor, given Ontario's population share has been > 35% since the 1970s. Admittedly other provinces have seen larger demographic shifts, but note that absolute player numbers are also biased to recent years (and I estimate well over half of all new players arrived on-ice since 1980).

With these caveats in mind, I present my first plot, which shows two sets of columns. The blue column is the expected number of players per province while red show the actual number. The scale is in powers of 2 to make smaller provinces more visible.

You may notice a bias towards athletes coming from the prairies and Ontario, while comparatively fewer from Atlantic Canada, Quebec and BC. One of the biggest positive outliers is Saskatchewan, who has contributed two and a half times more players than expected (480 compared to an expected 148).

Moving on to the finer resolution of small-town Canada, Saskatchewan looks to be a promising source of data.

Canadian prairies, mapping the birthplace of all Canadian NHL players. Image still taken from here.

As with previous analysis, I compared Saskatchewan's total population to the fraction of expected players per city/town/village. We expect by sheer random luck that a more populous urban centre ought to have more players. Saskatoon accounts for about 20% of the province's population. Have 0.20*478 = 96 players so far called this city their home? Let's find out.

There are far too many towns to map as a bar chart (over 100 total), so instead I created a logarithmic scatter plot.

The solid line is what you would expect for a 'perfect' distribution of on-ice hockey talent. As you can see, the larger cities (Saskatoon, Regina) do appear to have about as many players as expected. Regina has had 87 players, compared to an expected 84. But as we go to smaller locations, we see significant positive divergence from the line. Many players originate in towns so small that, statistically, it makes no sense for any players to have ever come from there. A few choice examples:

Swift Current (pop. 15,000): 10 NHL players (all from 1980 or earlier). Incidentally, it is also the home of recently-retired CIS championship runner Kelly Wiebe. On top of this, it's also a baseball powerhouse, home of three MLB players.

Flin Flon, MB (pop. 5,500) Technically not SK, but is literally one mile from the border. It has an unbelievable 17 former NHL players, including hall of famer Bobby Clarke.

There is an absence of medium-sized towns with players (read: suburbia). And places with no players are not shown in the plot. Adding the population together for locations with at least 1 player yields 680,000. Implicitly, then, there are other locations totalling 400,000 people that collectively have far less (NHL) talent than expected. Also interesting is that below a certain town size of about 1000-2000 people, there seems to be an even weaker correlation with talent and population size. One may consider the an adage along the lines of 'it takes one village, no more or less, to raise an athlete'.

My argument is that, statistically-speaking, talent comes from many small towns, as well as a few large ones, and few in between.

Before I finish, it might be argued I'm cherry picking from the past, when more people lived in Saskatchewan and the NHL was > 90% Canadian. Perhaps the small-town bias is no-longer true. To answer that, I turn to modern data of active-only NHL players (as of the 2015 season) superimposed on the original graph:

There are currently about 35 active NHL players born in Saskatchewan. And if anything, the small-town bias is even stronger. There are about half as many players coming from 'big' cities (8 vs an expected 16), hence more small town heroes than ever. My favourite example is the town special service area (?) Aneroid SK, with a population of 45 (forty five is not a typo), home to Patrick Marleau. A second-overall draft pick in the late 90s, and with over 1,300 games played so far, he is no slouch within the NHL. For that matter, how did Kindersley (pop. 4,700) produce 9 NHL players, two of which are still active? That's twice as many as Prince Albert (pop 35,000). What is in their drinking water?

The only explanation I can understand comes back to the original quote. "If you're good in a small town, everybody knows it and you have enormous self-confidence... I can really do all these things." Intuitively we might believe this already, but it's even more amazing to see it in the numbers. Small towns really do produce big talent.

If you do have skills, young enough, and live in suburbia, consider running away to a small town instead of the more cliched NYC approach. But whatever you do, please don't stay where you are.